Simultaneous diagonalization of incomplete matrices and applications

Abstract: We consider the problem of recovering the entries of diagonal matrices $U_a$ for $a = 1, \cdots, t$ from multiple “incomplete” samples $W_a$ of the form $W_a = P*U_a*Q$, where $P$ and $Q$ are unknown matrices of low rank. We devise practical algorithms for this problem depending on the ranks of $P$ and $Q$. This problems finds its motivation in cryptanalysis: we show how to significantly improve previous algorithms for solving the approximate common divisor problem and breaking CLT13 cryptographic multilinear maps.

cryptography and securityalgebraic geometrynumber theory

Audience: researchers in the topic

( chat | paper | slides | video )

Comments: The slides used in the pre-recorded video can be found here.

Chairs: Claus Fieker and Elena Kirshanova

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Algorithmic Number Theory Symposium (ANTS XIV)

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